I decided to delete everything and reinstall dsl on the stick just to make sure I didn't forget something along the way. I installed GRASS and QGIS from apt-get. GRASS worked, but not QGIS because of the same reason (libXrandr.so.2 missing). That seems strange to me because it was working the first time without the use of dpkg all the debs. So I decided to try different repositories where the softwares were available. QGIS didn't work using two repositories, but finally decided to work with:

The explanation is out of my reach. Anyway, I put PATH="$PATH:/mnt/sdb2/opt/jre1_5_0/bin" as the last line of /home/dsl/.bashrc as you suggested and now, guess what, EVERYTHING IS WORKING FINE! I get to the directory where my java app is and just launch it. Perfect.